3Atomic and molecular vibrations correspond to excited energy levels in quantum mechanicsEnergy levels are everything in quantum mechanics.Excited levelDE = hnEnergyGround levelThe atom is vibrating at frequency, ν.The atom is at least partially in an excited state.For a given frequency of radiation, there is only one value of quantum energy for the photons of that radiationTransitions between energy levels occur by absorption, emission and stimulated emission of photons

4Excited atoms emit photons spontaneouslyWhen an atom in an excited state falls to a lower energy level, it emits a photon of light.Excited levelEnergyGround levelMolecules typically remain excited for no longer than a few nanoseconds. This is often also called fluorescence or, when it takes longer, phosphorescence.

5Absorption spectra of moleculesHypothetical molecule with three allowed energy levelsNote relationship to emission!νij = ΔEij/hallowed transitionspositions of the absorption lines in the spectrum of the moleculeLine positions are determined by the energy changes of allowed transitionsLine strengths are determined by the fraction of molecules that are in a particular initial state required for a transitionMultiple degenerate transitions with the same energy may combine

10Interaction of radiation with matterWavelengthIf there are no available quantized energy levels matching the quantum energy of the incident radiation, then the material will be transparent to that radiation

11X-ray interactionsQuantum energies of x-ray photons are too high to be absorbed by electronic transitions in most atoms - only possible result is complete removal of an electron from an atomHence all x-rays are ionizing radiationIf all the x-ray energy is given to an electron, it is called photoionizationIf part of the energy is given to an electron and the remainder to a lower energy photon, it is called Compton scattering

12Ultraviolet interactionsNear UV radiation (just shorter than visible wavelengths) is absorbed very strongly in the surface layer of the skin by electron transitionsAt higher energies, ionization energies for many molecules are reached and the more dangerous photoionization processes occurSunburn is primarily an effect of UV radiation, and ionization produces the risk of skin cancer

13UV SO2 and O3 absorption spectraAbsorption cross-section represents the probability that a photon will be absorbed by a molecule of gas. TOMS Wavelengths not perfectly placed for SO2 as it is an Ozone instrument. Wavelengths are UV, Huggins bands. Spectral resolution affects our ability to resolve SO2 band structure and hence SO2 sensitivity and noise.

14Ultraviolet interactionsUV-A: nmUV-B: nmUV-C: nmThe ozone layer in the upper atmosphere absorbs most harmful UV radiation before it reaches the surfaceHigher UV-B frequencies are ionizing radiation and can produce harmful effects such as skin cancerThe ionosphere is a region of the upper atmosphere ionized by solar radiation

16Infrared (IR) interactionsQuantum energy of IR photons ( eV) matches the ranges of energies separating quantum states of molecular vibrationsVibrations arise as molecular bonds are not rigid but behave like springs

18Molecular dipole momentsFor a molecule to absorb IR radiation it must undergo a net change in dipole moment as a result of vibrational or rotational motion.The electric dipole moment for a pair of opposite charges of magnitude q is the magnitude of the charge times the distance between them, with direction towards the positive charge.The total charge on a molecule is zero, but the nature of chemical bonds is such that positive and negative charges do not completely overlap in most molecules. Such molecules are said to be polar because they possess a permanent electric dipole moment.Water is a good example of a polar molecule:Molecules with mirror symmetry like oxygen, nitrogen and carbon dioxide have no permanent dipole moments.

19Molecular polarizabilityThe polarizability of an atom or a molecule is a measure of the ease with which the electrons and nuclei can be displaced from their average positions (e.g., by an external electric field)When the electrons occupy a large volume of space, e.g., in an atom or molecule with many electrons, the polarizability of the substance is large. When an atom or molecule has large polarizability the magnitude of the instantaneous dipole can be large.The polarizability of molecules is important in Raman spectroscopy, based on Raman scattering.

20Key atmospheric constituentsDiatomic, homonuclear molecules (e.g., N2, O2) have no permanent electric dipole moment (also CO2)Molecular N2, the most abundant atmospheric constituent, has no rotational absorption spectrumOxygen (O2) has rotational absorption bands at 60 and 118 GHzLinear and spherical top molecules have the fewest distinct modes of rotation, and hence the simplest absorption spectraAsymmetric top molecules have the richest set of possible transitions, and the most complex spectraNote lack of permanent electric dipole moment in CO2 and CH4No

23Infrared (IR) interactionsVibrational transitions are associated with larger energies than ‘pure’ rotational transitions.Vibrations can be subdivided into two classes, depending on whether the bond length or angle is changing:Stretching (symmetric and asymmetric)Bending (scissoring, rocking, wagging and twisting)Stretching frequencies are higher than corresponding bending frequencies (it is easier to bend a bond than to stretch or compress it) Bonds to hydrogen have higher stretching frequencies than those to heavier atoms. Triple bonds have higher stretching frequencies than corresponding double bonds, which in turn have higher frequencies than single bonds

25Absorption spectra of moleculesV = Vibrational quantum numberJ = Rotational quantum numberElectronic, vibrational and rotational energy levels are superimposedThe absorption spectrum of a molecule is determined by all allowed transitions between pairs of energy levels, and whether the molecule exhibits a sufficiently strong electric or magnetic dipole moment (permanent or otherwise) to interact with the radiation field

32Absorption line shapesDoppler broadening: random translational motions of individual molecules in any gas leads to Doppler shift of absorption and emission wavelengths (important in upper atmosphere)Pressure broadening: collisions between molecules randomly disrupt natural transitions between energy states, so that absorption and emission occur at wavelengths that deviate from the natural line position (important in troposphere and lower stratosphere)Line broadening closes gaps between closely spaced absorption lines, so that the atmosphere becomes opaque over a continuous wavelength range.

33Pressure broadeningAbsorption coefficient of O2 in the microwave band near 60 GHz at two different pressures. Pressure broadening at 1000 mb obliterates the absorption line structure.

34Rovibrational EnergyVibrational and rotational transitions usually occur simultaneously splitting up vibrational absorption lines into a family of closely spaced linesRotational energy also dependent on direction of oscillation of dipole moment relative to axis of symmetryWhen oscillates parallel, ΔJ = 0 transition is forbidden and only P and R branches are seenWhen oscillates perpendicular, P, Q and R branches are all seenThe rotational constant is not the same in different vibrational states due to a slight change in bond-length, and so rotational lines are not evenly spaced in a vibrational bandRovibrational transitions in a CO2 moleculeDiagram taken from Patel (1968)

43Which is the most potent greenhouse gas?Top: SF6 (sulfur hexafluoride); global warming potential ~23000 times that of CO2 over a 100 year period. SF6 is extremely long-lived as it is inert (lifetime of years)

44Ozone (O3)Ozone is primarily present in the stratosphere except anthropogenic ozone pollution which exists in the troposphereAsymmetric top → similar absorption spectrum to H2O due to similar configuration (nonlinear, triatomic)Strong rotational spectrum of random spaced linesFundamental vibrational modes14.3 μm band masked by CO2 15 μm bandStrong v3 band and moderately strong v1 band are close in frequency, often seen as one band at 9.6 μm9.6 μm band sits in middle of 8-12 μm H2O window and near peak of terrestrial Planck functionStrong 4.7 μm band but near edge of Planck functionsoooosymmetric stretchv1 = 9.01 μmbendv2 = 14.3 μmasymmetric stretchv3 = 9.6 μm

51Mineral and rock reflectance spectraElectronic transitions in solids; Fe2+ (iron) particularly important in remote sensing – minerals contain Fe2+ ionsFundamental vibrational modes of H2O: 2.74 µm, 6.25µm, 2.66 µmIn rock spectra, whenever water is present we see 2 absorption bands in near-IR spectra – one near 1.45 µm (2ν3 overtone) and one near 1.9 µm (v2+v3 combination). Sharpness of bands relates to sites in crystal structure occupied by the water molecules.Note that penetration depth into natural surfaces is usually restricted to the upper few microns. Consequences?

53Why are most plants green and then red or yellow in the fall?Chlorophyll absorbs in the red and blue, and hence reflects in the green.Its absorption spectrum is due to electronic transitionsDuring spring and summer, leaves get their green cast from chlorophyll, the pigment that plays a major role in capturing sunlight. But the leaves also contain other pigments whose colors are masked during the growing season. In autumn, trees break down their chlorophyll and draw some of the components back into their tissues. Conventional wisdom regards autumn colors as the product of the remaining pigments, which were finally unmasked. In other words, autumn leaves were a tree's gray hair.But in recent years, scientists have recognized that autumn colors probably play an important role in the life of many trees. Yellow leaves get their color from a class of pigments called carotenoids. Another group of molecules, anthocyanins, produce oranges and reds. Trees need energy to make carotenoids and anthocyanins, but they cannot reclaim that energy because the pigments stay in a leaf when it dies. If the pigments did not help the tree survive, they would be a waste. What's more, leaves actually start producing a lot of new anthocyanin when autumn arrives."The reds are not unmasked-they are made in autumn," said Dr. David Lee, a botanist at Florida International University.Evolutionary biologists and plant physiologists offer two different explanations for why natural selection has made autumn colors so widespread, despite their cost. Dr. William Hamilton, an evolutionary biologist at Oxford University, proposed that bright autumn leaves contain a message: they warn insects to leave them alone.Dr. Hamilton's "leaf signal" hypothesis grew out of earlier work he had done on the extravagant plumage of birds. He proposed it served as an advertisement from males to females, indicating they had desirable genes. As females evolved a preference for those displays, males evolved more extravagant feathers as they competed for mates.In the case of trees, Dr. Hamilton proposed that the visual message was sent to insects. In the fall, aphids and other insects choose trees where they will lay their eggs. When the eggs hatch the next spring, the larvae feed on the tree, often with devastating results. A tree can ward off these pests with poisons.Photo and notes text borrowed from the NY Times.Plot borrowed from Peter v. Sengbusch -Comment from Ron Fox regarding the missing green absorption of chlorophyll:First off for the visual system, rod cells have an absorption max at 510 nm, i.e in the green. The three cone cells have maxima at 445, 545 and 585. All peaks are broad but the one at 545 is called the green cone. Thus the visual system has evolved to use what the plants don't use. Blue-green algae and red algae have pigments that do use the green ( ) missed by chlorophyll. The solar spectrum today at sea level is monotonically decreasing from a high at 700 to a low at 400, as far as the visible is concerned. The green part is less than the red part but by only a bit. A younger sun that was cooler would still be strong in the red but less so in the green. However, there is debate about the young sun's surface temperature. Chlorophyll a and chlorophyll b have complementary absorptions in separate portions of the red, suggesting that evolution tried to do as well as possible with the red.In the fall, trees produce carotenoids, which reflect yellow, and anthocyanins, which reflect orange and red.

54Why Mars looks redIron oxides prevalent in Martian soil show increased reflectance at the red end of the visible spectrum.

57Light excites atoms, which emit light that adds (or subtracts) with the input light.When light of frequency w excites an atom with resonant frequency w0:Electric field at atomElectron cloudEmitted field+=Incident lightEmitted lightTransmitted lightOn resonance (w = w0)An excited atom vibrates at the frequency of the light that excited it and re-emits the energy as light of that frequency.The crucial issue is the relative phase of the incident light and this re-emitted light. For example, if these two waves are ~180° out of phase, the beam will be attenuated. We call this absorption.

58Refractive Index vs. WavelengthSince resonance frequencies exist in many spectral ranges, the refractive index varies in a complex manner.Electronic resonances usually occur in the UV; vibrational androtational resonances occur in the IR; and inner-shell electronicresonances occur in the x-ray region.n increases with frequency, except in anomalous dispersion regions.